Quantum Field Theory

  1. Symmetries and Symmetry Breaking
    1. Global Symmetries
      1. Continuous Global Symmetries
        1. Lie Group Symmetries
          1. Noether Currents and Charges
            1. Conservation Laws
            2. Discrete Symmetries
              1. Parity Transformation
                1. Spatial Inversion
                  1. Parity Violation
                  2. Charge Conjugation
                    1. Particle-Antiparticle Exchange
                      1. C-Violation
                      2. Time Reversal
                        1. Motion Reversal
                          1. T-Violation
                        2. CPT Theorem
                          1. Statement and Proof Outline
                            1. Consequences for Particle Physics
                              1. CPT Violation Tests
                            2. Spontaneous Symmetry Breaking
                              1. Mechanism of Spontaneous Breaking
                                1. Degenerate Vacua
                                  1. Vacuum Expectation Values
                                    1. Order Parameters
                                    2. Goldstone's Theorem
                                      1. Massless Goldstone Bosons
                                        1. Number of Goldstone Bosons
                                          1. Non-linear Realizations
                                          2. Linear Sigma Model
                                            1. O(N) Symmetry Breaking
                                              1. Pions as Goldstone Bosons
                                            2. Gauge Symmetries and Higgs Mechanism
                                              1. Local Gauge Symmetries
                                                1. Gauge Transformations
                                                  1. Gauge Invariant Lagrangians
                                                  2. Higgs Mechanism
                                                    1. Spontaneous Breaking of Gauge Symmetry
                                                      1. Mass Generation for Gauge Bosons
                                                        1. Higgs Boson
                                                          1. Unitary Gauge
                                                          2. Abelian Higgs Model
                                                            1. U(1) Gauge Theory with Higgs
                                                              1. Massive Photon
                                                              2. Non-Abelian Higgs Mechanism
                                                                1. Yang-Mills-Higgs Theory
                                                                  1. Mass Matrix for Gauge Bosons
                                                                2. Chiral Symmetry
                                                                  1. Chiral Transformations
                                                                    1. Left and Right-Handed Fermions
                                                                      1. Chiral Symmetry in QCD
                                                                      2. Chiral Symmetry Breaking
                                                                        1. Quark Condensates
                                                                          1. Chiral Perturbation Theory
                                                                          2. Pseudo-Goldstone Bosons
                                                                            1. Pions in QCD
                                                                              1. Explicit Symmetry Breaking
                                                                            2. Anomalies
                                                                              1. Classical vs Quantum Symmetries
                                                                                1. Symmetry Breaking by Quantum Effects
                                                                                  1. Triangle Diagrams
                                                                                  2. Axial Anomaly
                                                                                    1. Axial Current Non-Conservation
                                                                                      1. Adler-Bell-Jackiw Anomaly
                                                                                      2. Chiral Anomaly
                                                                                        1. Fermion Determinant
                                                                                          1. Index Theorem
                                                                                          2. Physical Consequences
                                                                                            1. π⁰ → γγ Decay
                                                                                              1. Anomaly Cancellation in Standard Model

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                                                                                          6. Functional Methods

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                                                                                          8. Non-Abelian Gauge Theories